Velocity, Acceleration, Car problem

In summary, to find the car's velocity at t = 0s, you can use the equations vf^2 - vi^2 and vf - vi to find vf + vi. Then, solve for vi and vf to get the velocity at t = 0s.
  • #1
M1ZeN
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Homework Statement


A car accelerates at 2.0 m/s^2 along a straight road. It passes two marks that are 30 m apart at times t = 4.0s and t = 5.0s. What was the car's velocity at t = 0s?


Homework Equations



There are some equations in the chapter that I have used for previous homework problems but for this one I'm not sure which one or ones to use.

(Vf)^2 = (Vi)^2 + 2ad
(d = distance)
a = vf - vi/t
d = vt + 1/2a(t)^2


The Attempt at a Solution



I have tried finding the initial velocity at t = 0s but I can't seem to find a way to utilize the other variables.

Thanks.

Daniel
 
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  • #2
Using the first equation, find vf^2 - vi^2.
Using second equation find vf - vi.
From these two equations, find vf + vi.
Solve the above two equations to get vi and vf.
Here vi is the velocity a the end of 4 second, From that you can find v0 at t = 0
 
  • #3


I would approach this problem by first defining the given variables and identifying the key equations that can be used to solve for the unknown variable, which in this case is the initial velocity.

Given:
Acceleration (a) = 2.0 m/s^2
Distance (d) = 30 m
Time (t1) = 4.0 s
Time (t2) = 5.0 s

Key Equations:
1. Velocity (v) = initial velocity (vi) + acceleration (a) * time (t)
2. Distance (d) = initial velocity (vi) * time (t) + 1/2 * acceleration (a) * (time (t))^2

To solve for the initial velocity (vi), we can use the first equation by substituting the given values:
v = vi + 2.0 m/s^2 * 4.0 s
v = vi + 8.0 m/s

Next, we can use the second equation by substituting the given values and the calculated value of vi from the first equation:
30 m = vi * 5.0 s + 1/2 * 2.0 m/s^2 * (5.0 s)^2
30 m = vi * 5.0 s + 25.0 m
vi * 5.0 s = 5.0 m
vi = 1.0 m/s

Therefore, the car's initial velocity at t = 0s is 1.0 m/s. This means that the car was already moving at a speed of 1.0 m/s before it started accelerating at 2.0 m/s^2.
 

1. What is the difference between velocity and acceleration?

Velocity is a measure of an object's speed and direction of motion, while acceleration is the rate at which an object's velocity changes over time. In simpler terms, velocity tells us how fast an object is going and in what direction, while acceleration tells us how much an object's speed or direction is changing.

2. How do you calculate velocity?

Velocity is calculated by dividing the distance traveled by an object by the time it took to travel that distance. This can be written as v = d/t, where v is velocity, d is distance, and t is time.

3. What is the equation for acceleration?

The equation for acceleration is a = (vf - vi)/t, where a is acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval.

4. How does acceleration affect a car's performance?

Acceleration is a crucial factor in a car's performance as it determines how quickly the car can increase its velocity. A higher acceleration means the car can reach higher speeds in a shorter amount of time. This is important for activities such as racing or merging onto a highway.

5. What is the relationship between velocity and acceleration?

Velocity and acceleration are closely related as acceleration is the rate of change of velocity. This means that a change in velocity will result in acceleration, and vice versa. For example, if a car is accelerating, its velocity will increase, and if it is decelerating, its velocity will decrease.

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